Uncertainty Quantification (UQ):
Since my PhD years, I have worked extensively on uncertainty quantification, with a focus on developing efficient numerical methods. My PhD study led to the development of generalized polynomial chaos (gPC) method.
A concise one-semester textbook on stochastic methods related to UQ was published by Princeton University Press in 2010.
Approximation Theory:
Multivariate approximation theory and algorithms related to (orthogonal) polynomials, Gaussian Process (GP).
Efficient sampling strategies and Design of Experiments (DoE)
Machine Learning for Scientific Computing:
Data driven modeling of dynamical systems. In particular, the flow map learning (FML) methods.
DNN modeling of Partial differential equations (PDEs)
Deep learning of stochastic differential equations (SDE)